[Day 4] 2. Diffie-Hellman Key Exchange

Algorithm to Generate Symmetric Key at Both Ends

The Diffie-Hellman Key Exchange algorithm is commonly used to establish a shared symmetric key between two parties over an insecure channel. Here's how it works:

Setup

Imagine Tinku and Pinki want to securely exchange a symmetric key.

Both agree on two public values:
1. Prime Number
  p
  : 23
2. Base
  g
  : 5

Step 1: Secret Integers

Tinku selects a private secret integer
a
: 6
Pinki selects a private secret integer
b
: 15

Step 2: Compute Public Values

Tinku calculates:

A = g ^ a mod  p

A = 5 ^ 6 mod  23 = 8

Pinki calculates:

B = g ^ b mod  p

B = 5 ^ 15 mod  23 = 19

Step 3: Exchange Public Values

Tinku sends A (8) to Pinki.
Pinki sends B (19) to Tinku.

Step 4: Compute Shared Secret Key

Tinku calculates the shared key

s = B ^ a mod  p

s = 19 ^ 6 mod  23 = 2

Pinki calculates the shared key

s = A ^ b mod  p

s = 8 ^ 15 mod  23 = 2

Result

Both Tinku and Pinki have independently computed the same shared symmetric key:
2
.
This symmetric key can now be used for secure communication.

Key Points

Confidentiality: The secret integers (
```
a
```
and
```
b
```
) are never transmitted, ensuring that the shared key is secure.
Shared Key: The same symmetric key (
```
2
```
in this example) is derived independently by both parties.
Scalability: This method allows secure key exchanges without requiring prior secure communication.